Power-law decay of homogeneous turbulence at low Reynolds numbers

The decay of nominally isotropic, homogeneous incompressible turbulence is studied by direct numerical simulations for Re-lambda in the range (5-50) with 256(3) spectral coefficients. A power-law decay of the turbulent energy is observed with exponents approximately equal to 1.5 and 1.25, apparently dependent on Re-lambda. A new complete similarity form for the double and triple velocity correlation functions, f(r,t) and k(r,t), is proposed for low to intermediate Re-lambda that is consistent with the Karmia-Howarth equation and the results of the numerical experiments. The results are also consistent with Saffman's proposed asymptotic behavior of f(r,t) for large separation r for runs with a decay exponent of 1.5. The so-called final period of decay is not observed.

[1]  A. Townsend,et al.  Decay of turbulence in the final period , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[2]  R. Rogallo.  Numerical experiments in homogeneous turbulence , 1981 .

[3]  A. Townsend,et al.  Decay of isotropic turbulence in the initial period , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  William K. George,et al.  The decay of homogeneous isotropic turbulence , 1992 .

[5]  Nagi N. Mansour,et al.  Decay of Isotropic Turbulence at Low Reynolds Number , 1994 .

[6]  S. Pope,et al.  An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence , 1988 .

[7]  G. Batchelor,et al.  Decay of vorticity in isotropic turbulence , 1947, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[8]  P. Saffman.  The large-scale structure of homogeneous turbulence , 1967, Journal of Fluid Mechanics.

[9]  Smith,et al.  Decay of vorticity in homogeneous turbulence. , 1993, Physical review letters.

[10]  T. Kármán,et al.  On the Statistical Theory of Isotropic Turbulence , 1938 .

[11]  G. I. Barenblatt,et al.  Similarity, Self-Similarity and Intermediate Asymptotics , 1979 .

[12]  L. F. G. Simmons,et al.  Experimental Investigation and Analysis of the Velocity Variations in Turbulent Flow , 1934 .

[13]  G. I. Barenblatt,et al.  On the theory of self-similar degeneracy of homogeneous isotropic turbulence , 1973 .

[14]  S. Orszag.  Numerical Simulation of Incompressible Flows Within Simple Boundaries. I. Galerkin (Spectral) Representations , 1971 .

[15]  Peter S. Bernard,et al.  The energy decay in self-preserving isotropic turbulence revisited , 1991, Journal of Fluid Mechanics.

[16]  T. Vrebalovich,et al.  Grid turbulence at large Reynolds numbers , 1966, Journal of Fluid Mechanics.

[17]  G. Batchelor.  Energy decay and self-preserving correlation functions in isotropic turbulence , 1948 .

[18]  Jackson R. Herring,et al.  Comparison of direct numerical simulations with predictions of two-point closures for isotropic turbulence convecting a passive scalar , 1982, Journal of Fluid Mechanics.

[19]  S. Corrsin,et al.  The use of a contraction to improve the isotropy of grid-generated turbulence , 1966, Journal of Fluid Mechanics.

[20]  Empirical Equations for the Structure of Isotropic Turbulence , 1983 .